Abstract: Equivalent analysis based on weapon effectiveness, which was conducted during 1960s-1970s by American scholars, provided scientific method for equivalent analysis of weapon system. But this principle can only be used under the given conditions, which was pointed out by American scholars. That how to judge solution existence of effectiveness equivalent model under given conditions and remove limit is always a difficult question of perplexing weapon system analysis. By the use of special matrix theory and set decomposition principle, weapon coordination model of weapon system of systems combat was established, down-triangle matrix standard model of efficacy matrix was obtained, the existence problems of effectiveness equivalent model solution was solved from this starting point, multi- effectiveness equivalent principle was raised, effectiveness equivalent model was expanded, all of which provide a new method for equivalent analysis of weapon system.

Key words: equivalent analysis of weapon system, equivalent analysis of weapon system, equivalent equivalent, multi- equivalent equivalent